26 research outputs found
A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel
The Trotter-Suzuki approximation leads to an efficient algorithm for solving
the time-dependent Schr\"odinger equation. Using existing highly optimized CPU
and GPU kernels, we developed a distributed version of the algorithm that runs
efficiently on a cluster. Our implementation also improves single node
performance, and is able to use multiple GPUs within a node. The scaling is
close to linear using the CPU kernels, whereas the efficiency of GPU kernels
improve with larger matrices. We also introduce a hybrid kernel that
simultaneously uses multicore CPUs and GPUs in a distributed system. This
kernel is shown to be efficient when the matrix size would not fit in the GPU
memory. Larger quantum systems scale especially well with a high number nodes.
The code is available under an open source license.Comment: 11 pages, 10 figure
Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid
We study the dynamics of phase transitions in the one dimensional
Bose-Hubbard model. To drive the system from Mott insulator to superfluid
phase, we change the tunneling frequency at a finite rate. We investigate the
build up of correlations during fast and slow transitions using variational
wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and
numerical simulations. We show that time-dependent correlations satisfy
characteristic scaling relations that can be measured in optical lattices
filled with cold atoms.Comment: 7+ pages, the Bogolubov section is completely rewritte
Sensitivity to perturbations in a quantum chaotic billiard
The Loschmidt echo (LE) measures the ability of a system to return to the
initial state after a forward quantum evolution followed by a backward
perturbed one. It has been conjectured that the echo of a classically chaotic
system decays exponentially, with a decay rate given by the minimum between the
width of the local density of states and the Lyapunov exponent. As the
perturbation strength is increased one obtains a cross-over between both
regimes. These predictions are based on situations where the Fermi Golden Rule
(FGR) is valid. By considering a paradigmatic fully chaotic system, the
Bunimovich stadium billiard, with a perturbation in a regime for which the FGR
manifestly does not work, we find a cross over from to Lyapunov decay.
We find that, challenging the analytic interpretation, these conjetures are
valid even beyond the expected range.Comment: Significantly revised version. To appear in Physical Review E Rapid
Communication
Measuring Spatial Subdivisions in Urban Mobility with Mobile Phone Data
Urban population grows constantly. By 2050 two thirds of the world population
will reside in urban areas. This growth is faster and more complex than the
ability of cities to measure and plan for their sustainability. To understand
what makes a city inclusive for all, we define a methodology to identify and
characterize spatial subdivisions: areas with over- and under-representation of
specific population groups, named hot and cold spots respectively. Using
aggregated mobile phone data, we apply this methodology to the city of
Barcelona to assess the mobility of three groups of people: women, elders, and
tourists. We find that, within the three groups, cold spots have a lower
diversity of amenities and services than hot spots. Also, cold spots of women
and tourists tend to have lower population income. These insights apply to the
floating population of Barcelona, thus augmenting the scope of how
inclusiveness can be analyzed in the city.Comment: 10 pages, 10 figures. To be presented at the Data Science for Social
Good workshop at The Web Conference 202
A city of cities: Measuring how 15-minutes urban accessibility shapes human mobility in Barcelona
As cities expand, human mobility has become a central focus of urban planning
and policy making to make cities more inclusive and sustainable. Initiatives
such as the "15-minutes city" have been put in place to shift the attention
from monocentric city configurations to polycentric structures, increasing the
availability and diversity of local urban amenities. Ultimately they expect to
increase local walkability and increase mobility within residential areas.
While we know how urban amenities influence human mobility at the city level,
little is known about spatial variations in this relationship. Here, we use
mobile phone, census, and volunteered geographical data to measure geographic
variations in the relationship between origin-destination flows and local urban
accessibility in Barcelona. Using a Negative Binomial Geographically Weighted
Regression model, we show that, globally, people tend to visit neighborhoods
with better access to education and retail. Locally, these and other features
change in sign and magnitude through the different neighborhoods of the city in
ways that are not explained by administrative boundaries, and that provide
deeper insights regarding urban characteristics such as rental prices. In
conclusion, our work suggests that the qualities of a 15-minutes city can be
measured at scale, delivering actionable insights on the polycentric structure
of cities, and how people use and access this structure.Comment: 32 pages, 7 figure
Many-spin quantum dynamics during cross polarization in 8CB
We analyze theoretically and experimentally the quantum dynamics of a three-spin-1/2 system during cross polarization (CP). Our analysis takes into account a Hamiltonian behavior for a carbon C-13 coupled to two protons H-1 while the coupling to a spin bath is treated in the fast fluctuation approximation. This model is applied to the methylene and biphenyl groups of the smectic and nematic phases of the liquid crystal 4-n-octyl-4(´)-cyanobiphenyl (8CB). Experimental data from standard CP, combined with our theoretical results, allow us to separate the homonuclear H-1-H-1 and heteronuclear H-1-C-13 residual dipolar couplings. These values are in good agreement with those obtained by using a combination of CP under Lee-Goldburg conditions and standard CP data. A well differentiated relaxation behavior among the two phases seems to indicate that while the extreme narrowing approximation is appropriate for the nematic phase, the description of the smectic phase requires consideration of the slow-motion limit.Fil: Chattah, Ana Karina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Alvarez, Gonzalo Agustin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche | Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche; ArgentinaFil: Levstein, Patricia Rebeca. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Cucchietti, Fernando M.. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Pastawski, Horacio Miguel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Raya, Jésus. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Hirschinger, Jérôme. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin
Direct observation of quantum criticality in Ising spin chains
We use NMR quantum simulators to study antiferromagnetic Ising spin chains
undergoing quantum phase transitions. Taking advantage of the sensitivity of
the systems near criticality, we detect the critical points of the transitions
using a direct measurement of the Loschmidt echo. We test our simulators for
spin chains of even and odd numbers of spins, and compare the experimental
results to theoretical predictions
Universality of the Lyapunov regime for the Loschmidt echo
The Loschmidt echo (LE) is a magnitude that measures the sensitivity of
quantum dynamics to perturbations in the Hamiltonian. For a certain regime of
the parameters, the LE decays exponentially with a rate given by the Lyapunov
exponent of the underlying classically chaotic system. We develop a
semiclassical theory, supported by numerical results in a Lorentz gas model,
which allows us to establish and characterize the universality of this Lyapunov
regime. In particular, the universality is evidenced by the semiclassical limit
of the Fermi wavelength going to zero, the behavior for times longer than
Ehrenfest time, the insensitivity with respect to the form of the perturbation
and the behavior of individual (non-averaged) initial conditions. Finally, by
elaborating a semiclassical approximation to the Wigner function, we are able
to distinguish between classical and quantum origin for the different terms of
the LE. This approach renders an understanding for the persistence of the
Lyapunov regime after the Ehrenfest time, as well as a reinterpretation of our
results in terms of the quantum--classical transition.Comment: 33 pages, 17 figures, uses Revtex